I'll talk about what i know, so mainly medieval times. The answer is no. For two reasons, mainly :

First, arrows tend to break or weaken when fired. THe impact on steel, rock or even bones may very well break the arrow or weaken it so it becomes useless if re-used. English late medieval army (XIVth-XVth century), for exemple, mass-produced arrows to feed the need of their longbowmen.

Second, their is not really a need for "personnal arrows". Basically, just grab and arrow and shoot at the other guy. Of course, that was a little more complicated, because of the various size, strenght and characteristics of bows, but trained archers could know easily if the arrow they had in hand could suit their weaponry. If it did, just shoot it. If not, don't bother with it.

Bonus : not easy to recover arrows when you fire them in volley in a general direction, when they are stomped by the ennmy cavalry (or even infantry), even when they are marked. It would have been lots of work for nothing.